from finite mathematics and its applications, question 6.5.60 A bridge hand cons
ID: 2939128 • Letter: F
Question
from finite mathematics and its applications,question 6.5.60 A bridge hand consist of 13 cards selectedfrom a deck of 52 cards.
a) how many possible bridge hands contain at least oneace? b) how many possible bridge hands contain the ace ofspades? c) let E = "the hand contains at least 2 aces"
Let F = "the hand contains at least one ace" Let G = "the hand contains the ace of spades"
WHich is the greater probability: P(E|F) or P (E|G)
question 6.5.60 A bridge hand consist of 13 cards selectedfrom a deck of 52 cards.
a) how many possible bridge hands contain at least oneace? b) how many possible bridge hands contain the ace ofspades? c) let E = "the hand contains at least 2 aces"
Let F = "the hand contains at least one ace" Let G = "the hand contains the ace of spades"
WHich is the greater probability: P(E|F) or P (E|G)
Explanation / Answer
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Question Details:
question 6.5.60 A bridge hand consist of 13 cards selectedfrom a deck of 52 cards. 13 CARDS CAN BE SELECTED FROM 52 IN 52C13 WAYS
TOTAL NUMBER OF POSSIBILITIES = 52C13 a) how many possible bridge hands contain at least oneace?
LET US TAKE THE CASE THAT THERE IS NO ACE ..
SO WE CAN PICK 13 FROM 52-4=48 CARDS ONLY IN 48C13 WAYS .
HENCE NUMBER OF HANDS HAVING AT LEAST ONE ACE = 52C13 - 48C13
b) how many possible bridge hands contain the ace ofspades?
THERE IS ONLY ONE SPADE ACE WHICH IS ALREADY SELECTED
SO WE HAVE TO SELECT 12 MORE FROM 51
NUMBER OF HANDS = 51C12
c) let E = "the hand contains at least 2 aces" Let F = "the hand contains at least one ace" Let G = "the hand contains the ace of spades" WHich is the greater probability: P(E|F) or P (E|G)
USE BAYS THOREM
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